On Development of Two-Wheeled Balancing Robot Adaptive Control System on Basis of Second Lyapunov Approach with Tunable Step Size

Abstract

The problem of a two-wheeled balancing robot control is the scope of this research. Such plants are unstable, and their mathematical description includes several types of nonlinearities: rising to the power of the robot state coordinates and the trigonometric functions application. Moreover, such objects are non-stationary, i.e. they change the values of their parameters (mass, position of the center of mass and the coefficient of friction of the wheels on the road surface). The existing control systems of balancing robots (in most cases, these are optimal LQ algorithms and PID controllers) are not able to provide compensation of significant parametric disturbances, although they have a certain robustness with respect to them. All above mentioned problems make it reasonable to apply adaptive control algorithms to such plants. So we propose an adaptive control system based on the second Lyapunov method and the use of a reference model. To build such an adaptive controller in this study: 1) a mathematical description of the reference dynamics of the robot (at nominal values of its parameters) is made; 2) the LQ regulator parameters are calculated according to the theory of optimal control; 3) an adaptation loop of the parameters of the obtained controller, which does not require the plant model, is developed on the basis of the second Lyapunov method. The resulting adaptation loop is supplemented with a variable step size, which is recalculated on the basis of data about the current and previous values of the reference of the robot state coordinates. Experimental validation of the adaptive controller is made with the help of both mathematical and physical models of the balancing robot. Considering the experiments with the mathematical model, the mass of the robot is increased from two to 13.5 times. As for the physical model, the mass is doubled. The experimental results show the efficiency of the developed system in comparison with the optimal LQ-regulator in terms of the integral quadratic transient quality index.